In the past, much effort has been devoted to developing efficient methods of performing computerized research. Recent efforts in this area have been aimed at reducing the time required to accomplish an efficient search, while still providing accurate results. These efforts, however have fallen short of expectations due to the complicated and time consuming calculations required.
In general database searching has been limited to a "boolean" search, whereby the user inputs a specific data or textual item and the search program performs a text by text analysis procedure. Only direct textual matches are retrieved for the user to evaluate. Not only is this type of search inefficient, but large amounts of irrelevant data may also be retrieved due to the nature of the search.
To solve this and other problems associated with a boolean type search, computerized search programs have evolved to search a database for relationships among the data. Once these relationships are identified, they can be quantified as Euclidean distances and output to a display, whereby the distance between the data points represents the magnitude of the relationship between all data points. However, the number of Euclidean distances usually far exceeds the number of degrees of freedom available for mapping the data points into the x-y plane. Therefore, in order to map the data elements to the x-y plane while preserving the Euclidean distances as much as possible, a least squares approach to mapping the points is used. When a large database consisting of n data elements and approximately n.sup.2 /2 conditions to be satisfied is encountered, a least squares approximation requires order n.sup.3 operations. For larger values of n this is a highly computation intensive process which requires a mainframe computer to process the data.